When Two and Two Make Four: A Structured Population Without Chaos

Because a large number of theoretical models suggest chaos in populations, field biologists have been trying for decades to confirm the existence of chaos in nature. In spite of their efforts, chaotically evolving populations have been found in extremely low numbers. In this article we consider a metapopulation model which was built up by the interaction of local populations. Local populations interact with their nearest neighbours via migrations, but migration occurs only if the local population density exceeds a threshold level (overcrowding). Depending on the strength of the interaction, the metapopulation density shows noiselike dynamics of many degrees of freedom, periodical evolution, or tends to a fixed point. Low dimensional collective chaos has not been detected. Moreover, the migration size distribution indicates the emergence of self-organized criticality, if the interaction is strong enough.